Measure the length and the width of the room. Multiply the length and the width to get the square footage of the room. Use this number to order you new plywood subfloor material.
Remove the tile from on top of the subfloor. Break ceramic tile with a hammer and pull upward.
Remove one line of vinyl tiles from the floor using a pry bar. Set the depth of a circular saw to a 1/2 inch and cut through the subfloor. Pry up the subfloor with a pry bar.
Lay down the new subfloor panels, staggering the joints so that no four corners meet, somewhat like a brick layout. Leave 1/32 of an inch between boards.
Secure the new flooring to floor joists using finishing nails every 6 inches.
Fill the gaps in the subfloor with a non-shrinking, quick-dry wood filler. This material is available at all hardware stores.